Geometric Sequences Practice

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

The common ratio (r) can be found by dividing any term in the sequence by the previous term: r = a_n / a_(n-1).

10, 30, 90, 270.

The nth term of a geometric sequence can be expressed as a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

12,288.

1, ¼, 1/16.

The recursive rule is written as a_1 = first term; a_n = a_(n-1) * r, where r is the common ratio.

¼.

a_3 = 64 * (¼)^(3-1) = 4.

Each term is obtained by multiplying the previous term by the common ratio.